mathsurgery - factors



	factors Edit 0 10 … 7 Tags division factorize factors integers learn properties of number year 7 Notify RSS Backlinks Source Print Export (PDF) factors of a number Table of Contents factors of a number Learning Objective: Investing: Preparing: Discovering: Modeling: Discussing: Explaining: Practicing: Sharing: Assessing: Developing: Learning Objective: we are learning to factorise (US spelling: factorize) an integer (whole number) success criteria: by the end of this lesson you will be able to find all the factors of any number between 1 and 100. Investing: This is useful because factors are at the heart of working with fractions factors help us find prime numbers factors help us simplify algebra and solve equations Functional (real-life) applications include bicycle technicians/designers want to make sure that cogs don't have common factor numbers of teeth so that cogs don't wear out so quickly and there is a better spread of available gear ratios. there's a lot of interesting mathematics in choosing and using the right gears for a bike: have a look at some of these sites: wikipedia - bike gearing the 'Gearing 101 Tutorial' on www.cyclingsite.com Mike Sherman's bicycle gear calculator Sheldon Brown seems to be something of an authority on this subject and he's posted a pdf of his article 'Gain Ratios: A new way to think about bicycle gears' some biologists are noticing patterns to do with factors in predator-prey relationships such as those demonstrated by these periodical cicadas Magicicada tredecim and Magicicada septendecim: If the life cycle of Magicicada tredecim is thirteen years and Magicicada septendecim only hatches once every 17 years, how long is it between occasions in which they both appear in the same year and compete for the same food sources? What if these were 15 years and 18 years instead? Is there something special about 13 and 17 years that makes these cicadas more likely to survive? What might be the role of 'factors of numbers' in the evolution of these species? when you buy a product in bulk, the product and packaging designers need to think about the factors of a number: you can package 12 bottles of smoothie into a crate much easier than 11, because you can arrange 12 bottles as 3 × 4 or 2 × 6, but with 11 bottles you don't get much choice - see the smoothie-box task at plans and elevations. This skill leads to: prime numbers prime factorization solving quadratic equations factorizing algebra simplifying fractions simplifying ratios adding and subtracting fractions A 'free gift' with this skill is that we can now also... This could help you if you want to work in... Preparing: Are we ready? Do you know almost all of your multiplication facts up to 10×10? Do you know the divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 10? Let's be sure you can recall muliplication facts. In class use mini-whiteboards or use this Excel tool for a little quiz on paper: random multiplication questions.xlsm Details Download 16 KB Before you start you need to know: You will have a deeper understanding if you also know: Discovering: Can you figure it out yourself from these examples? Try to predict the next one aloud or on a mini-whiteboard. Investigate... Modeling: Here are some examples of people getting it right: Here are some examples of people getting it wrong in typical ways: Here are some more examples. Did they get it right or wrong? Explain how you know! Discussing: What would this one be? Tell your learning partner. Convince them you're right. Explain how you know. How would you explain this to someone who was new to it? Explaining: One way to do this is... Another approach might be... A useful shortcut is to... This works because... It doesn't work when... An exception is... Watch out for... A common mistake is... You can check your result by... We can prove this works by... Practicing: Some straightforward examples. Some harder examples. Some mixed examples. Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data. You can demonstrate fluency by at least... Sharing: A web page or wiki I have created to explain this can be found at... A presentation I have created and rehearsed looks like... A poster I have drawn or model I have made can be found... Assessing: Check you've mastered this skill by... Show you understand by explaining... Prove you're an expert in... by... Developing: Next we could learn... This leads to... Now try... last edited: Jul 29, 2011 12:36 pm help on how to format text

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